{
  "id": "1207.6170",
  "version": "v1",
  "published": "2012-07-26T05:16:12.000Z",
  "updated": "2012-07-26T05:16:12.000Z",
  "title": "Relations in the 24-th homotopy groups of spheres",
  "authors": [
    "Toshiyuki Miyauchi",
    "Juno Mukai"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The main purpose of this note is to give a proof of the fact that the Toda brackets $<\\bar{\\nu},\\sigma,\\bar{\\nu}>$ and $<\\nu,\\eta, \\bar{\\sigma}>$ are not trivial. This is an affirmative answer of the second author's Conjecture (Determination of the $P$-image by Toda brackets, Geometry and Topology Monographs 13(2008), 355-383). The second purpose is to show the relation $\\bar{\\nu}_7\\omega_{15}=\\nu_7\\sigma_{10}\\kappa_{17}$ in $\\pi^7_{31}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-26T05:16:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q40",
      "55Q50"
    ],
    "keywords": [
      "homotopy groups",
      "toda brackets",
      "second authors conjecture",
      "second purpose",
      "topology monographs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6170M"
    }
  }
}